宇宙中的暗物质湮灭会产生大量的高能正电子,正电子的质量为m,电量为e,通过寻找宇宙中暗物质湮灭产生的正电子是探测暗物质的一种方法(称为“间接探测”)。如图所示是某科研攻关小组为空间站设计的探测器截面图,粒子入口的宽度为d,以粒子入口处的上沿为坐标原点建立xOy平面直角坐标系,以虚线AB、CD、EF为边界,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
区域有垂直纸面向外的匀强磁场,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ed%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
区域有垂直纸面向里的匀强磁场,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
区域内磁感应强度的大小均为B;
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ed%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
区域有沿y轴负方向的匀强电场,电场强度大小为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ee%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmi%3Em%3C%2Fmi%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
处放置一块与y轴平行的足够长的探测板PQ。在某次探测中,仅考虑沿x轴正方向射入的大量速度不等的正电子,正电子的重力以及相互作用不计,其中一些正电子到达边界AB时,速度与x轴的最小夹角为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmn%3E30%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,对此次探测,求: